* rwg <rwg@sdf.org> [Dec 26. 2015 14:40]:
[...]
_____________
http://jjj.de/tmp-xmas/thin-3-tiles-sty1.pdf switches from L-system: 2 iterations axiom = _F_+F_+F sty = 3 1 0 F |--> F+F0F+F-F+F0F0F+F-F+F-F+F0F0F0F+F-F+F-F+F-F+F0F0F0F-F+F-F+F-F+F-F0F0F0F-F+F- F+F-F0F0F-F+F-F0F-F # mk-thin-3-dragon.gp: R48-1 # dragon # symm-dr to L-system: 2 iterations axiom = _F_+F_+F sty = 3 1 0 F |--> F+F0F+F-F+F0F0F+F-F+F-F+F0F0F0F+F-F+F-F+F-F+F0F0F0F0F-F+F-F+F-F+F-F0F0F0F-F+F- F+F-F0F0F-F+F-F0F-F # mk-thin-3-dragon.gp: R49-1 # dragon # symm-dr about 1/3 of the way in. It starts out identically(?) to a base 2+omega system where the omega^1, omega^3, and omega^5 digits of "France" are replaced with larger ones, producing a feathery tile. --rwg
Not sure I understand. One can take _any_ tile for the smallest surrounded sets (the very many tiny triangles, which one can render as hexagons). Choosing one tile for those "atoms" corresponds to the tile of a product curve (two iterates of the curve we are looking at, followed by one iterate of "whatever", as in my Section 5). Every curve has a tile, we can multiply curves, hence tiles. The tiles shown in thin-3-tiles-sty1.pdf correspond to two families of curves, each with again two sub-families.
From my file: Family 1: orders 3,4, 12,13, 27,28, 48,49, 75,76, 108,109, ... Family 2: orders 7,9, 19,21, 37,39, 61,63, 91,93, 127,129, ...
And yes, switching back and fourth between orders written next to each other is somewhat lovely (stare at the center of the image to get the difference beyond rotation). Btw. the "manta" curves show that curves exists that move without any turn as long as theoretically possible (_one_ more straight move and they'd be at the end point!). Best regards, jj
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun